Chad Andrews-Fulton added 21 points on 7-of-9 shooting for the Eagles (2-19, 2-4 Mid-Eastern Athletic Conference), who won for the second time in four games after opening the season 0-15.
The game, which featured nine ties and 13 lead changes, was knotted at 25 at halftime and it was 64-all at the end of regulation after Morgan State's Phillip Carr hit two free throws with six seconds left.
The Bears (7-12, 3-3) grabbed a 66-64 lead on a Stanley Davis layup 43 seconds into the extra period, but Davis pulled Coppin State even with two free throws and Cedric Council gave the Eagles the lead for good on a dunk with 3:30 left. Coppin State hit 10 of 12 free throws in overtime to preserve the victory.
The Eagles' only other win this season was a 79-78 double-overtime victory over Florida A&M that snapped a 20-game losing streak dating back to last season.
Tiwian Kendley topped the Bears with 26 points, but he made just 10 of 26 from the floor, including 1 of 7 from 3-point range, and had seven turnovers.